Fractional Fourier domains
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The well-known uncertainty principle dictates that 1/4π is a lower bound on the time-bandwidth product of a signal, and only the Gaussian signal has a time-bandwidth product equal to this lower bound.
“The well-known uncertainty principle dictates that is a lower bound on the TBP of a signal, and only the Gaussian signal has a TBP equal to this lower bound [21].”
From Short-time fourier transform: two fundamental properties and an optimal implementation (2003) · cites this paper as [21]
The paper’s uncertainty relation (section C161, Eq. 9; page unavailable in our copy) gives a lower bound on the product of variances and says it reduces to the familiar function–Fourier-transform relation for orthogonal domains. This supports the time–bandwidth lower-bound part, although the equation is OCR-corrupted in our copy. The paper does not state that only Gaussian signals attain the bound. (LLM, conf=0.82)
Experimental — accuracy not yet measuredThe STFT satisfies the rotation property only if its window function is a Hermite-Gaussian function.
“Proposition 1: STFT satisfies the rotation property only if the window function is a Hermite-Gaussian function.”
From Short-time fourier transform: two fundamental properties and an optimal implementation (2003) · cites this paper as [21]
The C161 section discusses rotation between fractional Fourier domains and projections of the Wigner distribution, but does not address the STFT window required for a rotation property. Searches for STFT, Hermite-Gaussian windows, and spectrogram rotation found no passage establishing the claimed 'only if' condition. Page numbers are unavailable in our copy. (LLM, conf=0.74)
Experimental — accuracy not yet measured
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Short-time fourier transform: two fundamental properties and an optimal implementation
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Self-citationFractional Fourier analysis using the mobius inversion formula
Miao, H., Zhang, F., & Tao, R. (2019) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2019.2912878 · Cited by 32 · see citing works
- Authors
- Ozaktas, H. M., & Aytür, O.
- Affiliations
- Bilkent University (TR)
- Venue
- Signal Processing
- Publisher
- Elsevier BV
- Published
- 1995-09
- Volume
- 46
- Issue
- 1
- Pages
- 119-124
- ISSN
- 0165-1684 (ISSN-L)
- OpenAlex
- W2128539777
- Cited by
- 141
- References
- 30
- Citations by year
- 2026: 3 · 2025: 2 · 2024: 4 · 2023: 5 · 2022: 4 · 2021: 7 · 2020: 3 · 2019: 7 · 2018: 7 · 2017: 5 · 2016: 6 · 2015: 8 · 2014: 3 · 2013: 7 · 2012: 5
- FWCI
- 4.51
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Signal Processing (publishedVersion)
- Bilkent University Institutional Repository (Bilkent University) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical Analysis and Transform Methods
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Engineering › Computational Mechanics › Sparse and Compressive Sensing Techniques
- Keywords
- fractional Fourier transform, time-frequency plane, uncertainty relations, commutation relations, time-frequency domain, signal representation, translation operators, differentiation operator
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